This invention relates to knowledge information processing systems by which neural networks providing functions corresponding to human intuitive thinking and logical thinking are combined, such that the knowledge information processing similar to that of the human brain can be realized.
The construction of neural network models is generally based on the following assumption. It is not the individual neurons within a living brain that store specific items of information. Each item of information is stored in a collection of a large number of neurons which cooperate with each other. Further, the information within the living brain is assumed to be processed as follows. The initial inputs to the respective neurons are repeatedly processed along the pattern of connections among the neurons. The pattern of connections among the neurons stores the information, and, when the information is processed within the brain, the individual neurons effect the calculations of the sum of input stimuli thereto and the threshold value processings. The system of the neurons spontaneously converge to a stable state (the low energy state of the system). The final stable state of the system represents the result of information processing.
The information stored in the brain or the neural network may be regarded as tile complete information. FIG. 3 is a diagram showing the variations of the energy state of a neural network system processing incomplete information. As shown in FIG. 3, when an arbitrary incomplete item of information (such as the letter "A", "J", or "E") is input to the neurons, the system of neurons converges spontaneously to a stored complete item of information at a minimal energy level (for example, the letter "A", "J", or "E") which is closest to the input item. The final stable state of the system of neurons may be regarded as the complete information which is output from the system. This is the principle of the knowledge processing by means of the associative memory in accordance with the neural network model.
Next, an implementation of the associative memory device according to a neural network model called Hopfield model is described.
FIG. 4 is a diagram showing a conventional optical implementation of an associative memory device according to the Hopfield model. The device is described, for example in: Material OQE 87-174, 1988, of the Research Committee of Optics and Quantum Electronics, the Institute of Electronics, Information and Communication Engineers of Japan.
In FIG. 4, the associative memory device includes: an input device 2, light-emitting element arrays 10a and 10b, optical masks 11a and 11b, light-receiving element arrays 12a and 12b, a differential amplifier 13, a comparator 14, and an output device 15. The operation of the device of FIG. 4 is as follows.
An item of input, such as the letter "A" of the English alphabet represented in a dot matrix, is input to the input device 2. The bits corresponding to the input are supplied from the input device 2 to the light-emitting elements 10a and 10b. Each element of the light-emitting element array 10a fans out a light beam to the corresponding row of the optical mask 11a. Similarly, each element of the light-emitting element array 10b fans out a light beam to the corresponding row of the optical mask 11b.
Let the state of k'th element of the light-emitting element array 10a or 10b be represented by X.sub.k (k=1, 2, . . . , n). The value "1" and "0" of X.sub.k corresponds to the ON and the OFF state of the k'th light-emitting element. The internal state of the light-emitting element array 10a or 10b is thus represented by a vector: EQU X=(X.sub.1, X.sub.2, . . . , X.sub.n)
where n is the number of elements of the light-emitting element array 10a, 10b or the light-receiving element array 12a, 12b; which corresponds to the number of neurons of the neural network.
The optical mask 11a and 11b are each divided into a matrix of n times n (n.times.n) elements. The transmittance of light of each element of the optical mask 11a and 11b can be varied individually. Let the values of transmittance of the elements of the optical mask 11a or 11b be represented by a matrix: T=(T.sub.ij), where T.sub.ij represents the transmittance of the (i,j)-element of the optical mask 11a or 11b. Further, let the internal state of the light-receiving element array 12a or 12b be represented by a vector U: EQU U=(U.sub.1, U.sub.2, . . . , U.sub.n)
The light emitted from the j'th light-emitting element of the light-emitting element array 10a or 10b irradiates the j'th row of the optical mask 11a or 11b. The light transmitted through the i'th column of the optical mask 11a or 11b is converged on the i'th light-receiving element of the light-receiving element array 12a or 12b. Thus, the vector U is a multiplication of the matrix T by the vector X: ##EQU1##
Within the neural network, the strengths of connections among the respective neurons bear the information stored therein. In this optical implementation, the strengths of connections among the neurons are represented by the transmittance matrix T of the n.times.n elements of the optical mask 11a or 11b. Namely, the transmittance matrix T of the optical mask 11a or 11b stores the information involved. If the number of items of stored information is represented by N, the information storage rule according to the Hopfield model is given by: ##EQU2## where T.sub.ij =T.sub.ji and T.sub.ii =0.
The elements T.sub.ij of the transmittance matrix T may take both positive and negative values. It is difficult, however, to process the negative values optically. Thus, the positive and negative values, T.sup.(+).sub.ij and T.sup.(-).sub.ij, of the matrix T are implemented separately by the optical mask 11a and 11b, respectively. Thus, the device of FIG. 4 includes two optical systems, indicated by the suffixes a and b, respectively, for processing the positive and negative values. The differential amplifier 13 obtains the difference of the outputs of the light-receiving elements 12a and 12b: EQU U.sub.i =U.sup.(+).sub.i -U.sup.(-).sub.i
The output of the differential amplifier 13 is fed back to the light-emitting element array 10a and 10b after the threshold processing by the comparator 14: EQU X.sub.i =.THETA.(U.sub.i)
where ##EQU3##
The optical masks 11a and 11b store, for example, three items of information corresponding to the letters, "A", "J" and "E". Thus, if an incomplete information "A"" is input to the input device 2, the input information is processed repeatedly and the system converges to "A", which is the closest to the input "A'". The complete item of information "A" is output from the output device 15.
This processing can be described as follows in terms of the energy of the system. The energy of the system is at minima at the stored items of information "A", "J", and "E". When an incomplete item of information is input to the system, the ON and OFF state of the light-emitting element array 10a and 10b changes such that the state of the system falls to the minimum energy state closest to the input state. The system thus spontaneously converges to a stored item of information closest to the input. This is similar to the association memory function of the human brain.
The above conventional knowledge information processing system, however, has the following disadvantage. Even if an inappropriate item is associated (i.e., even if the system converges to an incorrect item), the result is not corrected. The device only provides the function to associate a pattern which exhibits the closest correlation to the input. Thus the device does not provide a function as versatile as the human brain and hence is limited in its application.